Chapter 11: Differential Equation Graphing 191
11DIFFEQ.DOC TI-89/TI-92 Plus: Differential Equation (English) Susan Gullord Revised: 02/23/01 11:04 AM Printed: 02/23/01 2:15 PM Page 191 of 26
Use the two coupled 1st-order differential equations:
y1' = ëy1 + 0.1y1 ùy2 and y2' = 3y2 ìy1 ùy2
where:
y1 = Population of foxes
yi1 = Initial population of foxes (2)
y2 = Population of rabbits
yi2 = Initial population of rabbits (5)
1. Use 3to set Graph = DIFF EQUATIONS.
2. In the Y= Editor ( ¥#),
define the differential
equations and enter the
initial conditions.
3. Press:
ƒ 9
— or —
TI-89: ¥ Í
TI-92 Plus: ¥ F
Set Axes = ON, Labels = ON,
Solution Method = RK, and
Fields = FLDOFF.
4. In the Y= Editor, press:
TI-89: 2‰
TI-92 Plus: ‰
Set Axes = TIME.
5. In the Window Editor
( ¥$), set the
Window variables.
t0=0. xmin=ë1. ncurves=0.
tmax=10. xmax=10. diftol=.001
tstep=p/24 xscl=5.
tplot=0. ymin=ë10.
ymax=40.
yscl=5.
6. Graph the differential
equations ( ¥%).
7. Press …to trace. Then press
3 ¸ to see the number of
foxes (yc for y1) and rabbits
(yc for y2) at t=3.
Example of Time and Custom Axes
Using the predator-prey model from biology, determine the
numbers of rabbits and foxes that maintain population
equilibrium in a certain region. Graph the solution using both
time and custom axes.
Predator-Prey Model
Tip: To speed up graphing
times, clear any other
equations in the Y= Editor.
With
FLDOFF
, all equations
are evaluated even if they
are not selected.
Tip: Use
C
and
D
to move
the trace cursor between th
e
curves for y1 and y2.
y1(t)
y2(t)